Slow light has a variety of applications, in particular for enhanced nonlinear effects like four-wave mixing and high-harmonic generation. Here, we propose a photonic crystal coupled-cavity waveguide with an ultracompact arrangement of the constituent cavities in the propagation direction, and use an optimization algorithm to tune several structural parameters to engineer slow light with a constant group index n(g) over a wide bandwidth. We propose several specific silicon designs, including one with n(g) approximate to 37 over a 20 nm wavelength range and another one with n(g) approximate to 116 over an 8.8 nm band, which yields a group index-bandwidth product of 0.66-a record value among all slow-light devices. The design is experimentally beneficial because of its small footprint and straightforward fabrication and could find applications in optical storage or switching, and in generating quantum states of light. (C) 2015 Optical Society of America